
for some sufficiently large \(c_2\) , so we can regard \((P_{1,N}(i),\Lambda _{1,N}(i))\)  as the solution of a scalar-valued quadratic BSDE on \([0,T]\)  for each \(i\in \mathcal {M}\) . Thus by Proposition 2.4 in [1]}, there exists a process \(\Lambda _1^T(i)\in L^2_{\mathcal {F}^W}(0,T;\mathbb {R}^n)\)  such that \((P_1^T(i),\Lambda _1^T(i))\)  is a solution to the \(i^{\mbox{th}}\)  equation in ESRE (REF ) on the time interval \([0,T]\)  with terminal value \(P_1^T(T,i)\) .
